As a result of a change in the state of energy, all matter greater than -273.15°C (0°K)
radiates energy in the form of electromagnetic radiation following **Stefan-Boltzmann's
Law**:

,

where *&epsilon* is emissivity
(*&epsilon* =1 for a perfect blackbody,
0.95 < &epsilon < 0.98
for most other non-blackbody objects), *&sigma* is a
constant equal to 5.67 10^{-8} W m^{-2}K^{-4} , *T* is the
temperature of the body in degrees centigrade, and *E* is the energy of
the body given in units of W m^{-2}. For example, for
a blackbody body such as the sun with a skin temperature of 5600°C, it's energy per unit area
equals approximately 6.74 10^{7} W m^{-2}. The wavelength (in µm) of maximum
emission for any non 0°K body is written as (**Wien's Displacement Law**):

,

thus, for example, the maximum emission wavelength of the sun is 4.9 10^{-1} µm (490
nm).

The earth receives the electromagnetic radiation from the sun (typically defined as shortwave radiation) and emits it at longer wavelengths (typically defined as longwave radiation). Figure 1 depicts the earth's shortwave (blue lines) and longwave (red lines) energy fluxes.

The spectral component (i.e. radiation vs. wavelength) of the blackbody's emissive power can
be computed using **Planck's Law**:

where *I* is the intensity of radiation (Wm^{-2}sr^{-1}) over an entire
hemisphere, *&lambda* is wavelength (m), *c* is the speed of light (2.99
10^{8} ms^{-1}), *h* is Planck's constant (6.626 10^{-34} J s)
and *k* is Boltzmann's constant (1.380658 10^{-23} Ws K^{-1}).

Note: The aforementioned equation will output intensity as a function of wavelength in µm. To determine the intensity as a function of wavelength at different wavelengths- say as nm- you must multiply the equation by the appropriate coefficient. |

__References:__

Bonan, Gordon. 2002. Ecological Climatology: Concepts and applications. Cambridge Press, United Kingdom, 678 pp.

Siegel, Robert and Howell, John R. 1968. Thermal radiation heat transfer: Volume 1, the blackbody, electromagnetic theory, and material properties. Office of Technology Utilization, NASA, 190 pp.